SOLUTION: Marc sold 563 tickets for the school play. Student tickets cost $4 and adult tickets cost $6. Marc’s sales totaled $2840. How many adult tickets and how many student tickets did Ma

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Marc sold 563 tickets for the school play. Student tickets cost $4 and adult tickets cost $6. Marc’s sales totaled $2840. How many adult tickets and how many student tickets did Ma      Log On


   

Question 215565: Marc sold 563 tickets for the school play. Student tickets cost $4 and adult tickets cost $6. Marc’s sales totaled $2840. How many adult tickets and how many student tickets did Marc sell?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Marc sold 563 tickets for the school play. Student tickets cost $4 and adult tickets cost $6. Marc’s sales totaled $2840. How many adult tickets and how many student tickets did Marc sell?

Step 1. Let x be the number of students tickets sold and let 4x be the dollar value of student tickets sold.

Step 2. Let 563-x be the number of adult tickets sold and let 6(563-x) be the dollar value of adult tickets sold.

Step 3. Given total sales is $2840, then 4x%2B6%28563-x%29=2840. The following steps will solve this equation:

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=269.
  • Graphical form: Equation 4x%2B6%2A%28563-x%29=2840 was fully solved.
  • Text form: 4x+6*(563-x)=2840 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+4x%2B6%2A%28563-x%29=2840+%29
    For tutors: simplify_cartoon( 4x+6*(563-x)=2840 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 4%2Ax%2B6%2A%28highlight_red%28+563+%29-x%29=2840.
Moved 563 to the right of expression
It becomes 4%2Ax%2B6%2A%28-x%2Bhighlight_green%28+563+%29%29=2840.
Look at 4%2Ax%2B6%2A%28-x%2B563%29=highlight_red%28+2840+%29.
Moved these terms to the left highlight_green%28+-2840+%29
It becomes 4%2Ax%2B6%2A%28-x%2B563%29-highlight_green%28+2840+%29=0.
Look at 4%2Ax%2Bhighlight_red%28+6%2A%28-x%2B563%29+%29-2840=0.
Expanded term 6 by using associative property on %28-x%2B563%29
It becomes 4%2Ax-highlight_green%28+6%2Ax+%29%2Bhighlight_green%28+6%2A563+%29-2840=0.
Look at 4%2Ax-6%2Ax%2Bhighlight_red%28+6+%29%2Ahighlight_red%28+563+%29-2840=0.
Multiplied numerator integers
It becomes 4%2Ax-6%2Ax%2Bhighlight_green%28+3378+%29-2840=0.
Look at 4%2Ax-6%2Ax%2Bhighlight_red%28+3378+%29-highlight_red%28+2840+%29=0.
Added fractions or integers together
It becomes 4%2Ax-6%2Ax%2Bhighlight_green%28+538+%29=0.
Look at highlight_red%28+4%2Ax+%29-highlight_red%28+6%2Ax+%29%2B538=0.
Eliminated similar terms highlight_red%28+4%2Ax+%29,highlight_red%28+-6%2Ax+%29 replacing them with highlight_green%28+%284-6%29%2Ax+%29
It becomes highlight_green%28+%284-6%29%2Ax+%29%2B538=0.
Look at %28highlight_red%28+4+%29-highlight_red%28+6+%29%29%2Ax%2B538=0.
Added fractions or integers together
It becomes %28highlight_green%28+-2+%29%29%2Ax%2B538=0.
Look at %28highlight_red%28+-2+%29%29%2Ax%2B538=0.
Removed extra sign in front of -2
It becomes %28-highlight_green%28+2+%29%29%2Ax%2B538=0.
Look at highlight_red%28+%28-highlight_red%28+2+%29%29%2Ax+%29%2B538=0.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes -highlight_green%28+2+%29%2Ax%2B538=0.
Look at highlight_red%28+-2%2Ax%2B538+%29=0.
Solved linear equation highlight_red%28+-2%2Ax%2B538=0+%29 equivalent to -2*x+538 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=269.

Universal Simplifier and Solver


Done!



With x=269 , the 563-x= 563-269=294.

Check dollar value...4*269+6*294=2840...which is a true statement

Step 4. ANSWER. The number of student tickets sold is 269 and the number of adult tickets sold is 294.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J